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Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_3779_Библиотеки_им_академика_М_И_Перельмана
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cardiac output under the conditions of the increased systolic arterial pressure. The
prolonged retention of excess blood leads to the permanent left ventricular dilatation and
its wall thickening. The hypertension causes an additional load to the heart. Cardiac work
increases and the oxygen requirement of the heart elevates, which may be a possible cause
of further ischemic events [57].
The persistently low arterial pressure (hypotension) results in insufficient blood and, thus,
oxygen and nutrients supply of the organs and tissues. Hypotension may be a reason of
dizziness, fainting, heart, endocrine, or neurological disorders. Hypovolemia (reduced
blood volume) is one of the main reasons of hypotension. It can result from hemorrhage,
insufficient fluid intake, and excessive fluid losses. The other reasons may include the use
of different medications (diuretics, vasodilators, alpha- or beta-blockers). The failure of
regulatory mechanisms may result in orthostatic hypotension, which occurs after a change
in body position.
Hemodynamic compensatory responses to the hypotension and hypovolemia include the
mechanisms of decreasing venous capacity, the increasing of cardiac contractility and rate,
and the mechanisms of increasing vascular resistance. The latter mechanism relates to the
blood centralization, which ensures perfusion of critical organs.
2.5.5 Vein thrombosis
Venous thromboembolism is a potentially fatal condition. Standard treatment includes
prompt administration of anticoagulation medications. In the absence of effective
anticoagulation, the risk of thrombosis recurrence, progression, or embolization is
estimated to be 50% in 3 months. For the patients with a contraindication to
anticoagulation, a mechanical interruption of the inferior vena cava with a filter is an
acceptable method for minimization of the embolic events. Possible indications for filter
installation include free-floating thrombus in deep veins, presence of a pulmonary
embolism, recurrent venous thromboembolism despite anticoagulation, venous
thromboembolism with reduced cardiopulmonary reserve, and chronic thromboembolic
pulmonary hypertension undergoing pulmonary endarterectomy [58]. Retrievable cava
filters can be used if temporary protection is needed. The accurate indications of the filter
installation are still discussed.
Development of proper endovascular devices is one of the modern challenges in
biomedical engineering. The installed device with trapped thrombus should minimize
hemodynamic perturbations in the vessel and drag damage to the vessel wall. This requires
optimization of the device shape, the choice of materials with suitable properties as well
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as the place and the method of the device fixation. Other important factors one has to
account for are the thrombus dissolving, the impact on the global circulation, and chemical
species transport in the case of dissoluble devices. Such analysis requires complex
multimodeling and multiscale computational techniques [59,60].
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Patient-specific geometric modeling
3.1 Introduction
This section briefly discusses the use of medical imaging in scientific research. The
overview of human-like phantoms development is followed by the introduction to patientspecific geometric modeling in biomedical applications.
3.1.1 Development of human-like phantoms for scientific research
The history of anthropomorphic models starts from the radiation dosimetry problems [61].
In the first half of the 20th century, so-called “material phantoms” were used for
experimental measurements. These are real models made of solid materials, with shape
and density close as possible to the shape and density of imitated anatomical structures.
The use of such models was expensive, the preparation of experiments required
considerable effort and time. Later in the 1960s, first “computational phantoms” appeared.
In these models the shape of anatomical structures is described mathematically, and each
domain is attributed with a set of specific properties, such as material density and
conductivity. The first mathematical models of human anatomy were developed in the Oak
Ridge National Laboratory. They were created using constructive geometry from the
combinations of primitives: planes, cubes, prisms, cylinders, spheres, cones, and ellipsoids
[62].
The use of primitives failed to provide an accurate representation of real anatomy.
However, it made possible the parameterization of anthropometric data in the description
of the phantom. This allowed researchers to obtain models that take into account age and
gender characteristics. Adjusting the model parameters helped to design a whole family of
phantoms of people of different ages and complexion.
Rapid development and active application of computer and magnetic resonance imaging
technologies lead to the emergence of a new method for constructing “computational
phantoms,” also called tomographic models. The method consists in identifying boundaries
between the organs and tissues depicted in the tomography images and further assigning
every image voxel (i.e., a three-dimensional pixel) to a particular anatomical part or structure.
Personalized Computational Hemodynamics. https://doi.org/10.1016/B978-0-12-815653-7.00003-8
Copyright © 2020 Elsevier Inc. All rights reserved.
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This process is called segmentation. We shall define it more precisely below. Compared with
methods based on the combination of primitives, this approach has its own problems:
1. Segmentation requires the input of medical images (results of examination) of the
patient. The availability of images may be limited due to the expensive hardware
needed for examination.
2. Typically available medical images do not cover the entire body; they are cropped to
specific regions, either due to hardware limitations or for other reasons such as keeping
the radiation dose limited.
3. The process of identifying tissue and organs borders is by far not straightforward and
time-consuming.
Despite this, the “computational phantoms” obtained by the segmentation method continue
to gain recognition due to their anatomical accuracy, which is important in many
applications. The problem of completely automatic segmentation at this moment remains
unresolved. We refer the reader to Refs. [61,63] for a comprehensive review of the
evolution of computational models of human anatomy.
3.1.2 Image-based patient-specific models
Personalized numerical simulations of physiological processes in the human body received
a great deal of attention over several last decades, and a vast number of models have been
described in the literature. Contemporary resolution of medical images and new algorithms
for their postprocessing allow us to develop high-resolution numerical models of various
processes at cellular, organ, and the whole-organism scale [64e68]. For a given imaging
data set, one is commonly interested in image segmentation, volume reconstruction, and
numerical discretization.
The cornerstone of medical image processing is the segmentation process that assigns
labels to the voxels. Each biomedical application imposes special restrictions on both the
input medical images and the output patient-specific model and, therefore, calls for a
specific class of 3D segmentation methods. Various medical image segmentation
techniques have been developed (see, e.g., Refs. [69e71]). The most promising fully
automatic segmentation methods belong to the class of atlas-based segmentation
techniques [72e74]. The patient-specific segmentation is obtained from the atlas of
presegmented images of other individuals. This atlas should contain enough different cases
for accurate mapping of the new patient data. Thus, the atlas-based approach requires a
large amount of manual segmentation by an expert for the preparation of atlases and the
development of algorithms dealing with big data. The application area of atlas-based
methods is, however, limited due to lack of the specialized presegmented atlases.
Semiautomatic or supervised segmentation technologies require some interaction with an
expert. They are used primarily for the segmentation of particular organs and tissues.
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3.2 Basics of medical imaging
This section covers medical imaging, in general. The specifics about heart and vessel
segmentation are covered in consequent sections. We start from the basic principles of
several medical images acquisition techniques. Then, we move to the underlying
representation of the image data sets and general operations with images.
3.2.1 Image modalities
One of the most widespread medical image acquisition techniques is an ultrasound
imaging, or ultrasonography (US). An ultrasound device emits high-frequency sound
waves in different directions and captures the reflected waves.
Ultrasonography is a low-cost, informative, safe, reliable, and accessible diagnostic
procedure. Several modes of ultrasound scanning are used conventionally. The B-mode
(brightness mode) represents ultrasound echo as two dimensional; it is the most commonly
used mode in medical diagnostics and study of morphological condition of organs and
tissues. The brightness represents the intensity of the echo. The transit time of the acoustic
pulse determines the distance and position of the echo.
Doppler ultrasonography mode is based on the Doppler effect. It is capable of movement
detection. The direction and speed of moving sample is calculated from the pulse
frequency shift. The computed velocity is color-coded (Color Doppler mode) and is
usually combined with B-mode images (duplex mode).
Typically the US device is applied from the outside of the body. However, the
intravascular ultrasound (IVUS) may be used to visualize the inner wall of blood vessels
using a miniaturized ultrasound probe introduced inside the vessels through the catheter.
Computed tomography (CT) scan is a tomography technique, which produces images of
the structures of the body. In CT, a beam of X-rays from multiple angles penetrates the
examined object and is recorded by sensitive radiation detectors. This information is
analyzed by computer using the Radon transform equations; the result of analysis is a
detailed image reconstruction of the examined object and its contents.
Computed tomography angiography (CTA) is a CT technique with additional contrast, e.g.,
iodine-based contrast agent, intravenously injected to highlight arterial and venous vessels
in the body.
Cone beam computed tomography (CBCT) differs from CT in the divergent conical shape
of X-ray beams. CBCT is widely used in diagnosis and treatment planning in
interventional radiology, patient positioning, and verification in image-guided radiation
therapy.
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In magnetic resonance imaging (MRI), a radio frequency pulse from powerful magnets
excites and polarizes hydrogen nuclei of water molecules. Following the pulse, the
radiowaves emitted from the protons relaxation are registered and analyzed during image
reconstruction. MRI is believed to have minimal side effects since it does not use the
ionizing radiation, unlike CT. A variety of different excitation and measuring protocols
result in several MRI modalities: T1-weighted (T1-MRI), T2-weighted (T2-MRI),
diffusion-weighted imaging, and dynamic contrast enhancement MRI.
In this chapter, we focus on CT and MRI techniques, which are able to provide threedimensional images. Both CT and MRI are sensitive to different tissue properties;
therefore, the CT and MRI images may differ significantly. CT images have low contrast
in soft tissues, since they are not dense and do not block X-rays. At the same time, MRI
produces excellent images of soft tissues, since MRI imaging uses the hydrogen nuclei,
which are abundant in fluid and fat of soft tissues.
3.2.2 Contrast enhancement protocols and phases
Contrast enhancement is used to improve the visibility and distinguishability of specific
organs, tissues, and blood vessels. Generally, an iodine-based radiocontrast agent is used.
Often, images are taken both with and without radiocontrast. The time interval between
contrast administration and image acquisition is standardized in specific protocols for
visualization of different organs and tissues. The main phases of CT enhancement are as
follows: without contrast (nonenhanced CT), early arterial, late arterial, portal, and late
phase. The contrast propagation starts from the arteries. Next, the organs that get their
blood supply from the arteries receive the contrast. The contrast propagates to the veins
and highlights the liver parenchyma. Later, all parenchyma organs and veins are enhanced.
Different contrast agents may be used for specific studies. Gadolinium is the key
component of the contrast material most often used in MRI exams; it alters the magnetic
properties of tissues and enhances the MRI images.
One can use oral contrast solutions for gastrointestinal tract enhancement in abdominal CT
images. In this case, barium sulfate contrast materials are commonly used; however, in
some cases, a plain water or milk may be used as an alternative.
3.2.3 The voxel-based representation of the medical images
Medical images are associated with virtual physical space inside the CT/MRI machines.
Image is exported as a three-dimensional N
the same size and represents a small h
throughout array by integer tuples ðk
N2 N3array of voxels. Each voxel has
1
h2 h3rectangular box. Voxels are indexed
1
; k2; k3Þ. Assume the indexes start from zero:
1
˛ ½0.N11; k2˛ ½0.N21; k3˛ ½0.N31:
k
1
We denote voxel spacing by h ¼ðh1; h2; h
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Patient-specific geometric modeling 35
T
Þ
, image dimensions by
3
N ¼ðN
; N2; N3ÞT; Ni˛ Z; i ˛ ½1.3;
1
and voxel coordinates by
k ¼ðk
; k2; k3ÞT; ki˛ Z; i ˛ ½1.3:
1
The physical coordinates of the first voxel are called the image origin; we denote it by
o ¼ðo
One can also think about the voxel k as the rectangular domain in ℝ
points x ¼ðx
; o2; o3ÞT.
1
1
; x2; x3Þ such that:
o
iþkihi
< xi< oiþðkiþ1Þhi; i ¼ 1; 2; 3:
3
consisting of all
We define the set of possible image indexes by P:
P ¼fkjk
˛ ½0.Ni1; i ¼1; 2; 3g:
i
Image dimensions, origin, and voxel spacing are the core information, which is
incorporated in the image auxiliary data.
Medical images are usually grayscale, so we can represent them as mappings G: P/ℝ.In
most cases, CT and MRI machines export the color intensity as an integer value, in which
case, one can assume G : P/Z.
Typically, MRI images have significant variation in intensity across patients and scanners.
This makes it hard or even impossible to determine a tissue-specific absolute intensity
numerical meaning, even within the same MRI protocol, body region, for images obtained
on the same scanner, and for the same patient.
The radiodensity in CT images is measured in Hounsfield units (HU). The Hounsfield
scale is a linear scale, such that the radiodensity of water is taken as zero HU, and
radiodensity of air is taken as 1000 HU. The Hounsfield scale clearly distinguishes lungs
with high negative values (900 to 500 HU), fat with small negative values (100 to
80 HU), and bones with high positive values (higher than þ200 HU). However, most of
other organs and tissues lie in one range of small positive values (þ10 to þ90 HU).
For computational purposes, the most memory efficient numerical type is an 8-bit integer.
However, due to its low resolution, it is mostly used only in the segmentation images. A
wider range is usually required for MRI and CT images. A signed 12-bit integer represents
values from 2048 to þ2047 and is suitable for most medical images. Each voxel can be
represented using 2 bytes in computer memory. Note that one can reduce the memory
usage by combining two 12-bit integers as 24-bit data and store it using 3 bytes.
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The following information is necessary to define the image: image origin, voxel spacing,
and the image as the mapping G. Additional image information is preferable, such as
protocol description, image acquisitionespecific parameters, patient orientation, patient
identifier, acquisition date and time, and other useful information. Digital Imaging and
Communications in Medicine (DICOM) was developed as a standard for storing and
transmitting medical images enabling the intercommunication between medical imaging
devices and applications. Usually, DICOM images are organized in a tree-like structure
with DICOMDIR file in the root, holding references to all other files. The DICOM
information model itself is hierarchical. The levels of the model are the Patient, Study,
Series, and Image/Instance level. 3D images may be saved as a stack of files, one per each
slice inside the Series directory. Each image file includes the header with all metadata
information, including Series identifier.
Other popular formats for working with image and segmentation data include Analyze
image data format, Neuroimaging Informatics Technology Initiative (NIfTI) file format,
Nearly Raw Raster Data (Nrrd) file format, and Insight Toolkit MetaImage (ITK
MetaImage) file format. In some cases, the stack of ordinary image files may be used.
However, in this case, the spatial information should be saved separately.
Most of the file formats support saving 2D and 3D images with signed/unsigned 8-bit and
16-bit integers, floats, and RGB tuples. The segmentation image may be saved in the same
format with unsigned 8-bit integer as voxel type.
3.2.4 Basic operations with images and masks
Consider an input grayscale image G, and assume that the intensities are integers or floats
if not stated otherwise. Segmentation images are denoted by S. Usually, all operations with
grayscale images can be applied to segmentation images as well. Segmentation images are
treated as nonnegative integer images, where zero value has a special meaningdthe
background label. The binary mask is a special case of a segmentation image with only
one label.
The basic arithmetic operations with images include addition, subtraction, and
multiplication. These operations are performed voxel-wise:
sumðG
diffðG
mulðG
Þ
; G
: k1G
1
2
; G2Þ: k1G1ðkÞG2ðkÞ;
1
; G2Þ: k1G1ðkÞ$G2ðkÞ:
1
The voxel-wise min and max operators are defined similarly:
minðG
; G
1
2
Þ
: k1minðG
1
ðkÞ
1
þ G
ðkÞ
; G
2
ðkÞ
ðkÞÞ
2
;
;
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maxðG1; G2Þ: k1maxðG1ðkÞ; G2ðkÞÞ:
The clipping operator is used to clip the intensity of the image to the range ½a; b:
clipðG; a; bÞ: k1maxða; minðGðkÞ; bÞÞ:
The threshold operator is used to extract regions with image intensity in the range ½a; b:
1; if GðkÞ˛ ½a; b
threshðG; a; bÞ: k1
0; otherwise:
Let us consider a special case of segmentation image, the binary mask image
M : P/f0; 1g. For simplicity of the following presentation, we will allow the binary
mask M to be used as a set of voxels:
k ˛ M5MðkÞ¼1:
In some cases, we need a complement of the binary mask:
M : k11 MðkÞ or M ¼ P=M:
Operators on sets can be easily replaced by voxel-wise operators:
M
X M2¼ minðM1; M2Þ¼mulðM1; M2Þ;
1
W M2¼ maxðM1; M2Þ:
M
1
We need some further notations. Let us start with the definition of adjacent voxels. For
each voxel, we introduce two sets of adjacent voxels. Set N
ðkÞ denotes the set of voxels
6
adjacent to voxel k and sharing a face; this connectivity rule is called 6-adjacency. Set
N
ðkÞ denotes the set of voxels adjacent to voxel k, and sharing either a face, or an edge,
26
or a vertex, this connectivity rule is called 26-adjacency.
We can rewrite these definitions in the following way:
X
N
ðkÞ¼(m
6
ðkÞ¼m
N
26
i¼1;2;3
max
i¼1;2;3
m
j
j
iki
m
iki
¼1);
j
¼1:
j
A subset of binary mask is called a connected component when all voxels inside this
component are connected with a path of 26-adjacent voxels. The classical algorithm to
enumerate all connected components in the binary mask uses two passes to mark voxels in
the same component by a unique label. An improved algorithm from Ref. [75] for labeling
connected component can be adopted to 3D binary images. The algorithm is based on
run-length encoding [76]. For convenience, the labels of the connected components may
be reordered from the largest to the tiniest component size.
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Several mathematical morphology operators are quite useful in image processing. Here,
we discuss the basic ones: dilation, erosion, opening, and closing. These operators are
closely related to Minkowski addition described in the following.
First, let us define an auxiliary set representing the index offsets of voxels in the
neighboring ball of radius r:
B
¼fkjkkkrg;
r
where indices may be negative, and k $ k is Euclidean norm of vector
kkk
¼k
2
1
þ k
2
2
þ k
1=2
2
.
3
The dilation of binary mask is the enlarging of the mask by substituting each voxel with
the ball. The results can be obtained as the Minkowski sum of the initial mask M and the
neighboring ball B:
M 4 B ¼fk þmjk ˛ M; m ˛ Bg:
The erosion of binary mask is the shrinking of the mask by keeping only voxels, which
neighborhood balls are inside the mask. This result may be obtained as a Minkowski
difference of the initial mask M and neighborhood ball B:
M.B ¼fkjk 4 B 4 Mg:
The opening of the binary mask is obtained by the erosion, followed by the dilation of the
resulting mask:
M + B ¼ðM.BÞ4B:
The closing of the binary mask is similar, but obtained by performing dilation first
followed by erosion:
M , B ¼ðM 4 BÞ.B:
Efficient computation of morphological operations for 3D images [77] is based on the
following theorem [78]:
A 4 B ¼ AWðsurfðAÞ4 BÞ;
where surf(A) is the boundary of A
.
The set B is sometimes called the kernel of the morphological operator.
3.3 Heart segmentation
This section covers the segmentation techniques for the heart. We discuss the segmentation
of heart cavities and myocardium. New technique for dynamic heart ventricles
segmentation using dynamic contrast-enhanced CT images is presented in the end of the
section.
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